The EU has had “a bellyful” of the Brexit process and wants to get a deal, Boris Johnson has told the BBC.

He told Laura Kuenssberg it was “fed up with endless delays” and wanted to move onto the next phase of trade talks.

Brexit would happen on 31 October, he insisted, despite a new law requiring an extension if there is no deal.

He also accused critics of Parliament’s suspension of talking “mumbo-jumbo”, saying suggestions it had stopped MPs from doing their job was “claptrap”.

On a visit to Luxembourg, Mr Johnson held talks with the European Commission President Jean-Claude Juncker, the EU’s chief Brexit negotiator Michel Barnier and the country’s prime minister Xavier Bettel.

He said he had been encouraged by the EU’s willingness to engage with the UK in their shared desire to avoid a no-deal exit but there had not been a “total breakthrough”.

But the European Commission said the PM had yet to present concrete proposals for it to consider and insisted any new plans had to be “compatible” with the existing withdrawal agreement, which has been rejected three times by MPs.

And there was confusion after Luxembourg prime minister Xavier Bettel held a press conference without Mr Johnson amid noisy protests by anti-Brexit protesters.

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Mr Bettel, who answered journalists’ questions standing next to an empty lectern, warned Mr Johnson “you can’t hold the future hostage for party political gain”.

It is understood that Mr Johnson cancelled his press conference because of the noise of protesters, after his request for it to be held inside was turned down.

‘New relationship’

After the working lunch with Mr Juncker, Mr Johnson told the BBC’s political editor he was “cautiously optimistic” about the state of negotiations and suggested the EU wanted to bring the two and half years of arguments about the terms of the UK’s exit to an end.

“I see no point whatever in staying on in the EU beyond October 31st and we’re going to come out. And actually that is what our friends and partners in the EU would like too.

“And I think that they’ve had a bellyful of all this stuff. You know they want to develop a new relationship with the UK. They’re fed up with these endless negotiations, endless delays.”

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Media captionLuxembourg’s PM spoke beside the empty podium where Boris Johnson was due to appear

While he was working “very hard” to get a deal, he said there would be no agreement unless the EU shifted its position on the backstop, the insurance policy to maintain an open border on the island of Ireland unless and until another solution is found.

“If we can’t get movement from them on that crucial issue, of whether the EU can continue to control the UK…we won’t be able to get it through the House of Commons, no way.”

He said there were a number of ideas under discussion which would allow the whole of the UK to leave the EU while protecting the integrity of the bloc’s single market, upholding the Good Friday Agreement and supporting the Irish economy.

‘Load of nonsense’

These, he said, included the use of technology to minimise border checks as well as the so-called Stormont lock, a mechanism to give Northern Irish politicians a say on the rules that applying to Northern Ireland whether they diverge from the rest of the UK.

“It is all doable with energy and goodwill,” he insisted.

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Media captionBoris Johnson: “We are now in the stage where we have to start really accelerating the work”

He said he would meet the Halloween deadline come what may, insisting that the UK would be “in very good shape” whether there was a deal or not.

But pushed on how he would get around the law requiring him to ask for an extension if there is no deal by 19 October, the PM did not explain how it would be possible.

Ahead of Tuesday’s Supreme Court hearing into whether the prorogation of Parliament was lawful, Mr Johnson defended the decision to suspend Parliament.

He described claims that Parliament was “being deprived of the opportunity to scrutinise Brexit” as “all this mumbo jumbo” and a “load of claptrap”.